Holographic Noncommutativity

TL;DR

This paper explores noncommutative gauge and string theories via supergravity duals, revealing invariance of key parameters under dualities and constructing supersymmetric noncommutative models from specific solutions.

Contribution

It demonstrates the invariance of noncommutative moduli under O(p+1,p+1) transformations and establishes conditions for S-duality in noncommutative theories.

Findings

Noncommutativity parameter remains constant along RG flows.

Open string metric and coupling are deformation independent.

Constructed N=1 supersymmetric noncommutative theories from specific supergravity solutions.

Abstract

We examine noncommutative Yang-Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p+1,p+1) transformations of Dp-branes. The action of the T-duality group implies that the noncommutativity parameter is constant along holographic RG-flows. The moduli of the noncommutative theory, i.e., the open string metric and coupling constant, as well as the zero-force condition are shown to be invariant under the O(p+1,p+1) transformation, i.e., deformation independent. We find sufficient conditions, including zero force and constant dilaton in the ISO(3,1)-invariant D3 brane solution, for exact S-duality between noncommutative Yang-Mills and open string theories. These results are used to construct noncommutative field and string theories with N=1 supersymmetry from the T^(1,1) and Pilch-Warner solutions. The latter has a non-trivial zero-force condition due to the warping.